{"id":"W2041066603","doi":"10.1063/1.2191361","title":"Discrete and continuous sine transform generalized to semisimple Lie groups of rank two","year":2006,"lang":"en","type":"article","venue":"Journal of Mathematical Physics","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":22,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Lie group; Discrete sine transform; Fundamental representation; Pure mathematics; Rank (graph theory); Sine; Simple Lie group; Discretization; Algebra over a field; Mathematical analysis; Fractional Fourier transform; Fourier transform; Lie algebra; Combinatorics; Fourier analysis","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002923372,0.0003787906,0.0003779384,0.0008264434,0.0003984635,0.001359708,0.0004817236,0.0004975442,0.002374244],"category_scores_gemma":[0.0007947523,0.0001242186,0.0004758525,0.0005050294,0.002231966,0.001352188,0.000755865,0.0008106913,0.0003835385],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003962511,"about_ca_system_score_gemma":0.0003494482,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003456821,"about_ca_topic_score_gemma":0.0003594847,"domain_scores_codex":[0.9998041,0.00004682538,0.000008634558,0.00002611509,0.00008288476,0.00003158077],"domain_scores_gemma":[0.9996918,0.00006666638,0.00006050244,0.00005798034,0.00004866294,0.0000744275],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00005505235,0.00003069319,0.0003676779,0.00003179495,0.00000780719,0.0002268709,0.0002215461,0.009282296,0.008218245,0.97031,0.0004180584,0.01083004],"study_design_scores_gemma":[0.00002490066,0.0001533717,0.0005763122,0.00001902889,0.000007801341,0.000835225,0.0002893732,0.1808676,0.005838952,0.8060095,0.005335733,0.00004224095],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5708408,0.000528857,0.3928061,0.0005210642,0.0002489644,0.00004647164,0.0001121946,0.0002329408,0.03466257],"genre_scores_gemma":[0.9582068,0.0002265186,0.03320862,0.00008236084,0.0001288052,0.00003091582,0.00008660003,0.0000508083,0.007978444],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002374244,"threshold_uncertainty_score":0.007942617,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02912656189997193,"score_gpt":0.3366395310332787,"score_spread":0.3075129691333068,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}